1. To solve this problem you must apply the formula for calculate the area of a regular hexagon given the apothem, which is shown below:
A=(Perimeter x Apothem)/2
2. You have the apothem, so you can calculate the perimeter. First, you have to know the lenghts of the sides:
Tan(30°)=x/√3
x=1
Side=2x
Side=2
Perimeter=2x6
Perimeter=12
3. Then, you have that the area of the base is:
A=(Perimeter x Apothem)/2
A=12x√3/2
A=6√3
A=10.39
B=10.39 cm²
The answer is: B=10.39 cm²
